Approximating Sumset Size
Anindya De, Shivam Nadimpalli, Rocco A. Servedio

TL;DR
This paper introduces a sublinear-time algorithm for estimating the size of sumsets in the Boolean hypercube, which is efficient and independent of the ambient dimension, unlike previous methods.
Contribution
It presents the first sublinear-time algorithm for sumset size estimation that works with oracle access and provides approximate results with high probability.
Findings
Algorithm's query complexity depends only on psilon, not on dimension n.
Provides psilon-approximate sumset volume with high probability.
Achieves efficiency through a novel approximation method.
Abstract
Given a subset of the -dimensional Boolean hypercube , the sumset is the set where addition is in . Sumsets play an important role in additive combinatorics, where they feature in many central results of the field. The main result of this paper is a sublinear-time algorithm for the problem of sumset size estimation. In more detail, our algorithm is given oracle access to (the indicator function of) an arbitrary and an accuracy parameter , and with high probability it outputs a value that is -close to for some perturbation of satisfying It is easy to see that without the relaxation of dealing with rather than , any algorithm for estimating…
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Advanced Graph Theory Research · Limits and Structures in Graph Theory
